LATTICE MAGNETIC WALKS

Sums of walks for charged particles (e.g. Hofstadter electrons) on a s quare lattice in the presence of a magnetic held are evaluated. Return ing loops are systematically added to directed paths to obtain the unr estricted propagators. Expressions are obtained far special values of the magnetic flux-per-plaquette commensurate with the flux quantum. fo r commensurate and incommensurate values of the flux, the addition of small returning loops does not affect the general features found earli er for directed paths. Lattice Green functions are also obtained for s taggered flux configurations encountered in models of high-T-c superco nductors.